Relativistic Jets Chechetkin VM 5/28/10 1
Object of simulation SS433 jets (1977) M87 jets (1918) Picture and radio observation Radio, X-ray and optical observations 0.26c, 3·10 11 km 0.8-0.9c, 5·10 16 km 5/28/10 2
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Object of simulation. SS433 in motion: bullets of matter The VLBA observations Movie (Mioduszewski, Rupen, Walker, & Taylor 2004) 5/28/10 4
Object of simulation Primary properties: Various types of objects (AGNs, microquasars) Jets have extremely high energetics. Flow is well collimated (approx. 10°) and its structure is preserved for large distances Flow consists mostly of individual bullets emitted more or less periodically. 5/28/10 5
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Main ways of modeling MHD models Resistive MHD (e.g. Chechetkin, Savel’ev, Toropin 1997) Ideal MHD Funnel in thick magnetized accretion disk (e.g. Komissarov 2007, 2008); Flows around thin magnetized accretion disk without external side accretion (e.g. Chechetkin et al 1995, 1997, Pudritz 1997, Ustyugova et al. 1999); Magnetically channelized outflows around thin magnetized accretion disk (present work). Models with radiation (Shapiro 1986, Icke 1989, Taijma 1998, Chechetkin, Galanin, Toropin 1999) Jets in supernovae( Chechetkin, 1998, 2002,2004 , 2006) 5/28/10 7
Basic equations of nonrelativistic MHD: - equation of state where (green members describe finite conductivity, red - dissipation) The basic assumption: 5/28/10 8
Previous works: MHD mechanism for collimation V.M. Chechetkin et all , 1995-2010. «A possible mechanism for the formation of molecular flows» Conditions: Model is described with non-ideal MHD equation system Accreting to the central body plasma is not magnetized and there is region with homogenous magnetic field around central object. Due to the non-perfect conductivity of plasma accreting matter diffuses to the magnetic field. Results: Along rotation axis of system the accelerating channel (funnel) is formed Plasma is able to penetrate inside this channel, it is source of jet matter A series of plasma density discontinuities driving along system axis of rotation obtained 5/28/10 9
F � c r r 2 r F � � g g o 30 5/28/10 10
Magnetic monopole 11
r (a) Poloidal flow velocity v ( r , z ) at a sequence of times, t 0 , 4 , , 24 , where t is measured in units of the rotation period of K = p r the inner edge of the disk.The lengths of the arrows are proportion al to v . Also the slow magnetoson ic surface (dot - dashed line), p the Alfven surface (dashed line), the fast magnetoson ic surface (long dashed line), and the boundary of the matter coming from the disk (solid line) are shown. (b) Level lines of the azimuthal velocity v � 5/28/10 12
(a) Poloidal magnetic lines. (b) Level lines of the toroidal magnetic field Three - dimentiona l views of a magnetic field line that starts from the disk at x 4 r , y 0 . After the outward twist propagatio n associated = = i with the head of jet, the field line becomes well collimated . 5/28/10 13
1995 5/28/10 14
" Free" Boundary " Force - Free" Boundary Modified " F.F." Boundary r r r r r ( ) ( ) F j B 0 B P rB 0 B r B B B � � � � � = � � = � P P P r � � � � acting in direction � � 5/28/10 15
Mach cone can be characteri sed by angle 2 , which is cross - section of � cone by the ( r , z ) - plane : ( ) ( v c )( v v ) v c 2 2 2 2 + � tg , where v - " casp" velocity 2 � = A S P C = Ap S v c ) ( ) ( v c v c 2 2 S + 2 2 2 2 � � A S P SM p FM 5/28/10 16
Model scheme z Outward boundary Accretion Magnetic field Gravitating central object r 0 Rotating thin perfectly conducting disk 5/28/10 17
Results: distribution of density and poloidal magnetic field 5/28/10 18
Results: gas pressure logarithm and streamlines log p The channel confined by the magnetic field is stable, and its characteristics vary only weakly with time. The channel walls are formed of unmagnetized plasma with a high density and pressure. Such walls provide possibilities for accelerating the matter due to the pressure of the central body radiation. 5/28/10 19
Results: axial magnetic field and streamlines The jet is well collimated: the B z channel has the shape of a cone with a non-linear track, whose angle to the z axis is about 10°. The shape of the channel resembles that of a Laval aerodynamical nozzle. The critical cross section is the region of stagnation of the accreting matter. 5/28/10 20
Results: instability of magnetic field lines under thin accretion disk (animation of magnetic field poloidal projection) 5/28/10 21
We use the pseudopote ntial of Paczynski - Wiita to describe the gravitatio nal field around a Schwardzsc hild black hole. GM 2 GM , where r , M - the mass of the black hole. � = � = g g 2 r r c � g Distributi ons of density and magnetic field ( r ) ( r ) � = �� keplerian GM � = r r r � g Boundary conditions . 1) 0 , 2 r r r : symmetric conditions ; � = � � g max � 2) 0 , r r and r 2 r : " free boundary conditions " ; � � � = = max g 2 � 3) , 2 r r r - the part of boundary w hich represents disk. � = � � g max 2 5/28/10 22 � � � H ( r , ) 0 , H ( r , ) 0 , ( r , ) 0 . = = � = r 2 � 2 2
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Previous works: MHD mechanism for collimation 5/28/10 25
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Previous works: acceleration of matter by radiation pressure Galanin M.P., Toropin Yu.M., Chechetkin V.M. The Radiative Acceleration of Matter Bullets in Accretion Funnels near Astrophysical Objects. (1997) The null-dimension model including ODE for bullet dynamics in radiation field considered. The existence of channel with hot region at the foundation makes conditions for individual bullets to be effectively accelerated by radiation and launched out of the system. Top speeds of bullets in conic funnel (depends on angle β and absorption coefficient r ) 5/28/10 27
Previous works: radiative acceleration and importance of the funnel walls X – distance between bullet and central object. V – bullet velocity. Continuous line – acceleration of bullet in the funnel with perfectly reflecting walls. Dotted line – acceleration of bullet without funnel. 5/28/10 28
v –velocity of the bubble, с - light speed, Р i n. .3 и Р ° n. 3 -pressures, which react on the bubble interior and outer face thereafter , G - gravitational constant 5/28/10 29
Characterized for radiant pressure on bubble`s wall P n,3 = e3 P 0, e3 = ∆ 3/ ∆ 5/28/10 30
Maximal velocity( v –velocity of the bubble/ с - light speed) r- reflection coe ffj cient β – opening angle Г 2 β = 0 0 β = 3° β = 5° β = 10° 0.0 0.456 0.486 0.506 0.556 0.2 0.490 0.525 0.547 0.599 0.4 0.532 0.570 0.595 0.648 0.6 0.582 0.626 0.651 0.701 0.8 0.652 0.697 0.721 0.763 0.9 0.700 0.745 0.765 0.800 5/28/10 31
0.3 1 3 10 33 г 2 τ = 0.1 0.0 0.151 0.247 0.380 0.467 0.486 0.486 0.524 0.3 0.171 0.278 0.427 0.547 0.547 0.6 0.199 0.323 0.490 0.599 0.625 0.626 0.9 0.251 0.403 0.597 0.713 0.744 0.745 Maximal velocity at opening angle ( β = 3°) при χ 3 = 0 (ratio of temperatures) , r 3 = r1 =0 r 2 г 3 = 0.0 г 3 = 0.3 г 3 = 0.6 г 3 = 0.9 rr 0.0 0.486 0.539 0.583 0.619 0.3 0.614 0.673 0.720 0.758 0.6 0.740 0.798 ' 0.841 0.874 0.9 0.872 0.918 0.948 0.967 Maximal velocity ( β = 3°) при χ 3 = 0.9, τ = 33 5/28/10 32
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